具有水平传播和环境传播的反应扩散传染病模型研究

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1849-1860.

具有水平传播和环境传播的反应扩散传染病模型研究

胡振祥,聂麟飞*()

^{新疆大学数学与系统科学学院乌鲁木齐 830017}

收稿日期:2022-01-07 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 聂麟飞 E-mail:lfnie@163.com;nielinfei@xju.com
基金资助:
国家自然科学基金(11961066);新疆维吾尔自治区自然科学基金(2021D01E12);新疆维吾尔自治区自然科学基金(2021D01C070)

Analysis of a Reaction-Diffusion Epidemic Model with Horizontal Transmission and Environmental Transmission

Zhenxiang Hu,Linfei Nie*()

^{School of Mathematics and System Sciences, Xinjiang University, Urumqi 830017}

Received:2022-01-07 Online:2022-12-26 Published:2022-12-16
Contact: Linfei Nie E-mail:lfnie@163.com;nielinfei@xju.com
Supported by:
the NSFC(11961066);the Natural Science Foundation of Xinjiang Uygur Autonomous Region(2021D01E12);the Natural Science Foundation of Xinjiang Uygur Autonomous Region(2021D01C070)

摘要/Abstract

摘要：

该文提出一类具有水平传播和环境传播的反应扩散传染病模型, 讨论模型的适定性, 包括解的全局存在性和一致有界性.进一步, 通过下一代算子的谱半径定义给出基本再生数$ {\mathcal R}_{0}$的精确表达式, 并利用单调动力系统理论和一致持续性理论研究模型的阈值动力学.

关键词: 反应扩散模型, 环境传播与水平传播, 标准发生率, 基本再生数, 一致持续性

Abstract:

In this paper, a reaction-diffusion epidemic model with horizontal transmission and environmental transmission is proposed. The well posedness of this model is investigated, including the global existence and uniform boundedness of the solution. Furthermore, the basic reproduction number ${\mathcal R}_{0}$ is defined by the spectral radius of the next generation operator. The threshold dynamics of the model is studied by using monotone dynamical systems theory and uniform persistence theory.

Key words: Reaction-diffusion model, Environmental transmission and horizontal transmission, Standard incidence, Basic reproduction number, Uniform persistence

中图分类号:

O175.21

胡振祥,聂麟飞. 具有水平传播和环境传播的反应扩散传染病模型研究[J]. 数学物理学报, 2022, 42(6): 1849-1860.

Zhenxiang Hu,Linfei Nie. Analysis of a Reaction-Diffusion Epidemic Model with Horizontal Transmission and Environmental Transmission[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1849-1860.

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